Which of the following orbitals has the highest energy?

Options

A. 5d
B. 5f
C. 6s
D. 6p

Explanation

To determine which of the given orbitals has the highest energy, we can use the concept of the (n + l) rule. The energy of an orbital is determined by the sum of the principal quantum number (n) and the azimuthal quantum number (l). The orbital with the highest (n + l) value has the highest energy.

### Step-by-Step Solution:

1. **Identify the Orbitals**: The orbitals we need to evaluate are 5D, 5F, 6S, and 6P.

2. **Determine the Values of n and l**:
- For **5D**:
- n = 5 (principal quantum number)
- l = 2 (for D orbitals)
- (n + l) = 5 + 2 = 7
- For **5F**:
- n = 5
- l = 3 (for F orbitals)
- (n + l) = 5 + 3 = 8
- For **6S**:
- n = 6
- l = 0 (for S orbitals)
- (n + l) = 6 + 0 = 6
- For **6P**:
- n = 6
- l = 1 (for P orbitals)
- (n + l) = 6 + 1 = 7

3. **Compare the (n + l) Values**:
- 5D: (n + l) = 7
- 5F: (n + l) = 8
- 6S: (n + l) = 6
- 6P: (n + l) = 7

4. **Identify the Highest Value**:
- The highest (n + l) value is 8 for the 5F orbital.

5. **Conclusion**: Therefore, the orbital with the highest energy among the given options is **5F**.

### Final Answer:
The orbital with the highest energy is **5F**.

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